PRP Records

Probable Primes Top 10000

(202632 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
60012^241670+14572750Lelio R Paula03/2012
60025^104074+5272745Lelio R Paula08/2014
6003(3^152466-5)/72472742Lelio R Paula06/2012
600420^55908-4172738Lelio R Paula01/2015
6005(73*10^72735+53)/972736Robert Price10/2015
600610^72730+22401172731Patrick De Geest05/2013
600710^72730-9972730Robert Price05/2011
60083*10^72723+6772724Robert Price11/2017
6009(11^69833+3^69833)/1472723Robert Price03/2013
6010(10^72723-79)/372723Robert Price10/2017
6011(88*10^72711-43)/972712Robert Price11/2015
60123^152379+28072704Lelio R Paula01/2015
6013(25*10^72703-241)/972704Robert Price01/2017
6014(47*10^72696+133)/972697Robert Price04/2017
601517^59077-9072692Lelio R Paula01/2015
601665^40096+5872691Lelio R Paula01/2016
6017(29*2^241446-1)/24572682Lelio R Paula01/2014
601911^69783-3840000072672Enzo Doria01/2013
60182^241409-11290372672Enzo Doria06/2014
6020(3^152287+1)/472659Paul Bourdelais04/2008
60213^152249-5672642Lelio R Paula01/2015
602210^72631+3772632Robert Price01/2011
602310^72631-881372631Patrick De Geest05/2013
6024(19*2^241254+1)/10172624Lelio R Paula08/2012
6025(9^76103+8^76103)/1772620Robert Price12/2012
60262^241220-11233772615Enzo Doria06/2014
6027(82*10^72612+449)/972613Robert Price02/2017
60282^241169-1579372600Enzo Doria04/2013
60299*10^72595+1172596Robert Kinser01/2017
6030(25*2^241048+1)/8972563Lelio R Paula08/2012
6031(22*10^72560+17)/372561Robert Price09/2015
60322^241032-2372558Lelio R Paula02/2012
603334485*10^72550+2^241004-372555Gilbert Mozzo12/2012
60342^241004-372550M. Frind & P. Underwood07/2002
603597*10^72522-372524Robert Price01/2017
6036(68*10^72516+7)/372518Robert Price03/2016
6037(78557*2^240844+1)/6372505Lelio R Paula06/2014
603867^39701-6672497Norbert Schneider11/2014
6039(185*10^72484+7)/372486Robert Price02/2017
6041(293*27^50631-1736)/1372473Curtis Bright05/2015
6040103^36005-10272473Norbert Schneider10/2016
604215^61616+8872467Lelio R Paula01/2015
604345^43831+272462Lelio R Paula05/2013
60442^240692-49238972456Paul Bourdelais03/2013
6045(646*10^72446-7)/972448Robert Price07/2016
60469*6^93083+772434Lelio R Paula10/2014
60472^240617-364572433Lelio R Paula05/2013
604811^69531-2400072410Enzo Doria12/2012
6049(22699*2^240396+1)/5572370Lelio R Paula06/2014
60506^92995+1372365Lelio R Paula01/2015
6051(11*10^72362-149)/372363Robert Price01/2017
6052(2^240381+3)/5165572358Lelio R Paula05/2012
60536^92974-5572348Lelio R Paula01/2015
60542^240295+1172337Lelio R Paula02/2012
6055(14*10^72326-53)/372327Robert Price12/2016
605615^61493-4672322Lelio R Paula01/2015
6057lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
60585*10^72302+972303Dmitry Domanov11/2010
6059(9787*2^240179-1)/26572303Lelio R Paula04/2015
606011^69419-312072293Enzo Doria12/2012
60614*10^72274-8372275Robert Price10/2017
606210^72267+3372268Robert Price01/2011
606310^72267-55394772267Patrick De Geest05/2013
606411^69389-138072262Enzo Doria12/2012
6065(16^60013-5^60013)/1172262Robert Price07/2013
60667^85507-3072262Lelio R Paula08/2014
6067(19*2^240026-1)/1572256Lelio R Paula02/2014
6068(3^151426-2)/66133772243Lelio R Paula06/2012
6069gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
60702^239863-11226772206Enzo Doria06/2014
60712^239853-11485372203Enzo Doria05/2015
6072(4*10^72174+149)/972174Robert Price03/2017
6074(2^239671+9)/29613172143Lelio R Paula05/2012
60732^239651-11066572143Enzo Doria05/2014
6075(29*2^239650-1)/330572140Lelio R Paula01/2014
6076241^30280+30280^24172128Norbert Schneider11/2014
6077(68*10^72120-23)/972121Robert Price10/2015
6078(9^75571+8^75571)/1772112Robert Price12/2012
6079(15*2^239530-1)/17372105Lelio R Paula01/2014
60802^239513-11251972101Enzo Doria06/2014
6081(10^72097+149)/372097Serge Batalov12/2014
60822^239442-655572080Lelio R Paula05/2012
60832*5^103106+372069Lelio R Paula10/2014
60842^239402-19772068Lelio R Paula02/2012
60852^239356-11187572054Enzo Doria05/2014
6086(38*10^72050-119)/972051Robert Price11/2016
60872^239339+1501572049Lelio R Paula01/2013
6088159^32728+272048Lelio R Paula05/2013
608915^61259-3872047Lelio R Paula01/2015
609092^36683-91^3668372038Robert Price08/2015
60912^239280+5461572031Lelio R Paula05/2012
6092(47*2^239267+1)/7772027Lelio R Paula04/2015
6093(85*10^72025-1)/372027Robert Price07/2017
60942^239236-9730572018Lelio R Paula05/2012
60952^239169+5971998Lelio R Paula02/2012
6096lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
6097(15*2^239171-1)/10630171994Lelio R Paula01/2014
6098(29^49211-1)/2871965Robert Price04/2012
6099(299*10^71963+1)/371965Robert Price11/2017
6101L(344293)71953Renaud Lifchitz09/2003
6100V(344293)71953Serge Batalov03/2015
61026*10^71951+771952Dmitry Domanov11/2010
61033^150798+4071949Lelio R Paula01/2015
61042^238961+9571935Lelio R Paula02/2012
61052^238936-40771927Yves Minet02/2012
61062^238923-2863571923Lelio R Paula05/2012
610710^71910+2511971911Patrick De Geest05/2016
610810^71910-80171910Robert Price04/2016
61092^238845-11265171900Enzo Doria06/2014
61102^238792-11124571884Enzo Doria05/2014
61116*7^85059+571884Lelio R Paula10/2014
61122^238752-11058971872Enzo Doria05/2014
611312^66581+771853Lelio R Paula07/2014
6114(7*2^238691+1)/4122971850Lelio R Paula06/2012
61154*3^150568-571840Lelio R Paula04/2014
61166^92301+6771825Lelio R Paula01/2015
61172^238568+9876533171817Jason Earls01/2009
61182^238541-11272371808Enzo Doria06/2014
61192^238529-1594971805Enzo Doria04/2013
61209*5^102721-871800Lelio R Paula10/2014
61212^238494-16571794Lelio R Paula02/2012
61222^238389-11090571763Enzo Doria05/2014
6123(145*10^71760-1)/971762Serge Batalov12/2014
61247^84913+506271760Mike Oakes02/2010
6125(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
61262^238268-9730571726Lelio R Paula05/2012
6127gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
61282^238235-11324771716Enzo Doria07/2014
61292*12^66450-5^6645071712Mike Oakes11/2010
6130(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
61312^238199-11181771706Enzo Doria05/2014
6132lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
61332^238144+9876533171689Jason Earls01/2009
613418^57102-426571679Enzo Doria03/2013
6135(73*10^71670-1)/971671Robert Price01/2015
61362^238081+1155*23808171670Henri Lifchitz02/2005
61372^238067-11192571666Enzo Doria05/2014
613836^46030+3571637Norbert Schneider04/2014
6139(74*10^71621+313)/971622Robert Price11/2017
61402^237905-9171617Lelio R Paula02/2012
6141(31*2^237902-1)/12371616Lelio R Paula01/2014
6142(15185*2^237866-1)/4396771605Lelio R Paula04/2015
6143(24737*2^237841+1)/2571601Lelio R Paula06/2014
61442^237846+129971599Lelio R Paula05/2012
61456^92004+19980171594Mike Oakes02/2011
6146159^32516+271581Lelio R Paula05/2013
61472^237781+85571580Lelio R Paula05/2012
61482^237720-407971561Yves Minet06/2011
61492^237698-11094571555Enzo Doria05/2014
61502^237695-11323971554Enzo Doria07/2014
61518*5^102362-971549Lelio R Paula10/2014
6152(4*10^71546-31)/971546Erik Branger05/2011
61532^237650+3771540Lelio R Paula02/2012
615418^56977-439171522Enzo Doria03/2013
6156(22699*2^237565+1)/413663771512Lelio R Paula06/2014
6155((1+sqrt(7)+sqrt(6))^48479-1)*((1+sqrt(7)-sqrt(6))^48479-1)*((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(771512Mike Oakes05/2009
6157(26*10^71503+7)/371504Erik Branger11/2013
6158(4*10^71498+173)/371499Robert Price01/2017
61593^149848+11071496Lelio R Paula11/2014
61602^237498+51371495Lelio R Paula05/2012
61612^237485+10771491Lelio R Paula02/2012
6162(2^237465+9)/241971481Lelio R Paula05/2012
61632^237439-11223771477Enzo Doria06/2014
61642^237407-978771467Lelio R Paula11/2009
61652^237383+7295371460Enzo Doria04/2016
616682^37337-81^3733771457Robert Price01/2015
6167(1017*2^237313-1)/1971441Lelio R Paula04/2015
61682^237311+19171438Lelio R Paula02/2012
61692^237280-5971429Lelio R Paula02/2012
617011^68564-9871403Lelio R Paula01/2015
61712^237173+7480171397Enzo Doria04/2016
617215^60697+5671386Lelio R Paula01/2015
61732^237118+17771380Lelio R Paula02/2012
61742^237110+6971378Lelio R Paula02/2012
617515^60690-5871377Lelio R Paula01/2015
6176(5*2^237125-1)/59985119171374Lelio R Paula01/2014
6177(3^149567+2)/53971359Lelio R Paula06/2012
6178(5*10^71357-143)/371358Robert Price04/2016
61792^237039-11462171356Enzo Doria05/2015
618012^66116-3771352Lelio R Paula02/2015
6181(3^149497+2^149497)/571328Jean-Louis Charton10/2010
61822^236941-6694571327Lelio R Paula05/2012
61832^236911-114771318Yves Minet10/2009
618465^39337+4271315Lelio R Paula01/2016
61856*10^71299+771300Dmitry Domanov11/2010
6186(25*2^236843+1)/375371295Lelio R Paula06/2012
618710^71291+1518771292Patrick De Geest03/2016
618910^71291-558730911971291Robert Price03/2015
618810^71291-27358171291Patrick De Geest03/2016
6190-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
6191(2^236738+9)/1371265Lelio R Paula05/2012
61925^101949+4271260Lelio R Paula07/2014
61935*10^71237+971238Dmitry Domanov11/2010
61942^236634-1602571234Enzo Doria04/2013
619571^38478+7071233Norbert Schneider12/2014
61969*7^84280+871226Lelio R Paula10/2014
6197(10^71223+59)/371223Serge Batalov12/2014
6198(15185*2^236569-1)/45371216Lelio R Paula04/2015
619951829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
62002^236528-17371203Lelio R Paula02/2012
62013*2^236511-571198Lelio R Paula04/2014
62022^236477-9971187Lelio R Paula02/2012
620311^68356-213071186Enzo Doria12/2012
620411^68355-312071185Enzo Doria12/2012
620536^45737-35^4573771181Robert Price10/2012
6206(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
62072^236432+2571174Lelio R Paula02/2012
62085^101818-1280671168Enzo Doria02/2013
6209(7*10^71166-457)/971166Robert Price09/2017
621065^39253+6271163Lelio R Paula01/2016
621139^44718+3871150Norbert Schneider05/2014
62122^236296-40771133Yves Minet02/2012
62132^236286-11771130Lelio R Paula02/2012
62142^236257-11119371121Enzo Doria05/2014
62157^84149-3671115Lelio R Paula08/2014
62162^236209-11212371106Enzo Doria06/2014
621718^56644-498571104Enzo Doria03/2013
6218(46*10^71077+521)/971078Robert Price08/2017
621921^53753+271074Ray Chandler08/2011
6220(86*10^71068-311)/971069Robert Price10/2017
62212^236081-11092371068Enzo Doria05/2014
6222(293*27^49642-1736)/1371058Curtis Bright05/2015
622365^39192+2271052Lelio R Paula01/2016
6224(439#+1)^397-439#^39771038Mike Oakes11/2010
62257^84050-271031Lelio R Paula09/2013
622620^54558-2370982Lelio R Paula01/2015
62272^235793-11255570981Enzo Doria06/2014
622849936!3-3^4993670981Robert Price08/2015
62292^235787-7879570979Lelio R Paula05/2012
6230Perrin(581132)70970Eric W. Weisstein02/2011
623114^61913-9770961Lelio R Paula01/2015
62322^235720+1632170959Yves Minet03/2010
62332^235718+1609570959Lelio R Paula05/2012
6234163841#+34993370957Nicolas PALAU11/2016
62352^235710+770956Lelio R Paula02/2012
6236(175^31627+1)/17670939Eric Chen10/2017
62372^235635-11208770934Enzo Doria06/2014
62392^235575-196570916Lelio R Paula05/2012
62386^91133+10170916Lelio R Paula01/2015
6240(21181*2^235505+1)/370898Lelio R Paula06/2014
6241(14*10^70896+211)/970897Robert Price11/2017
62425^101425+8470894Lelio R Paula07/2014
6243177^31536+270893Lelio R Paula05/2013
624443*71^38292+470891Serge Batalov03/2016
6245(29*2^235506-1)/11202978570888Lelio R Paula01/2014
624611^68045-153070862Enzo Doria12/2012
62475*10^70858+2170859Robert Price01/2017
62482^235326+370841Donovan Johnson02/2006
624934523!2+470841Robert Price02/2015
6250(31*2^235307+1)/370836Lelio R Paula06/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

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